On topologies generated by some operators
Open Mathematics (2013)
- Volume: 11, Issue: 2, page 349-356
- ISSN: 2391-5455
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topKatarzyna Flak, and Jacek Hejduk. "On topologies generated by some operators." Open Mathematics 11.2 (2013): 349-356. <http://eudml.org/doc/269697>.
@article{KatarzynaFlak2013,
abstract = {The paper concerns topologies introduced in a topological space (X, τ) by operators which are much weaker than the lower density operators. Some properties of the family of sets having the Baire property and the family of meager sets with respect to such topologies are investigated.},
author = {Katarzyna Flak, Jacek Hejduk},
journal = {Open Mathematics},
keywords = {Lower density operator; Abstract density topology; Meager sets; Family of sets having the Baire property; lower density operator; density topology; Baire property of set},
language = {eng},
number = {2},
pages = {349-356},
title = {On topologies generated by some operators},
url = {http://eudml.org/doc/269697},
volume = {11},
year = {2013},
}
TY - JOUR
AU - Katarzyna Flak
AU - Jacek Hejduk
TI - On topologies generated by some operators
JO - Open Mathematics
PY - 2013
VL - 11
IS - 2
SP - 349
EP - 356
AB - The paper concerns topologies introduced in a topological space (X, τ) by operators which are much weaker than the lower density operators. Some properties of the family of sets having the Baire property and the family of meager sets with respect to such topologies are investigated.
LA - eng
KW - Lower density operator; Abstract density topology; Meager sets; Family of sets having the Baire property; lower density operator; density topology; Baire property of set
UR - http://eudml.org/doc/269697
ER -
References
top- [1] Ciesielski K., Larson L., Ostaszewski K., I-Density Continuous Functions, Memoirs of Amer. Math. Soc., 1994, 107, #515 Zbl0801.26001
- [2] Filipczak M., Filipczak T., On f-density topology, Topology Appl., 2008, 155(17–18), 1980–1989 http://dx.doi.org/10.1016/j.topol.2007.04.024 Zbl0468.26002
- [3] Filipczak M., Hejduk J., On topologies associated with the Lebesgue measure, Tatra Mt. Math. Publ., 2004, 28(2), 187–189 Zbl1107.54003
- [4] Hejduk J., Density Topologies with Respect to Invariant ρ-Ideals, University Press, Łódz, 1997
- [5] Hejduk J., On the density topologies generated by functions, Tatra Mt. Math. Publ., 2008, 40, 133–141 Zbl1199.54018
- [6] Hejduk J., Horbaczewska G., On I-density topologies with respect to a fixed sequence, In: Real Analysis Conference, Rowy, 2003, Wyzsza Szkoła Informatyki, Łódź, 2004, 78–85
- [7] Hejduk J., Wiertelak R., On the density topologies with respect to the sequences of intervals tending to zero, preprint available at http://www.math.uni.lodz.pl/preprints,all.html Zbl1329.26007
- [8] Lukeš J., Malý J., Zajíček L., Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Math., 1189, Springer, Berlin, 1986 Zbl0607.31001
- [9] Oxtoby J.C., Measure and Category, 2nd ed., Grad. Texts in Math., 2, Springer, New York-Berlin, 1980 http://dx.doi.org/10.1007/978-1-4684-9339-9
- [10] Poreda W., Wilczynski W., Topology similar to the density topology, Bull. Soc. Sci. Lett. Łódz Sér. Rech. Déform., 2001, 34, 55–60 Zbl1088.54500
- [11] Terepeta M., Wagner-Bojakowska E., ψ-density topology, Rend. Circ. Mat. Palermo, 1999, 48(3), 451–476 http://dx.doi.org/10.1007/BF02844336 Zbl0963.26003
- [12] Wiertelak R., A generalization of the density topology with respect to category, Real Anal. Exchange, 2006/07, 32(1), 273–286 Zbl1243.54008
- [13] Wilczyński W., A generalization of density topology, Real Anal. Exchange, 1982/83, 8(1), 16–20
- [14] Wilczyński W., Density topologies, In: Handbook of Measure Theory, North-Holland, Amsterdam, 2002, 675–702 http://dx.doi.org/10.1016/B978-044450263-6/50016-6 Zbl1021.28002
- [15] Wilczyński W., Aversa V., Simple density topology, Rend. Circ. Mat. Palermo, 2004, 53(3), 344–352 http://dx.doi.org/10.1007/BF02875727 Zbl1194.26002
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